I just have node.js with the TypeScript module pre-installed on the build server. It's not the most ideal solution, but it works. I have put together a quick CI starter project up on my GitHub to help people who are trying to do this very thing. You can
find it here: TypeScript-CI-Starter. The project uses Gradle for build automation and PhantomJS to run the Jasmine tests. It also generates JUnit xml reports so it can be easily consumed by a
CI server. This seems to work pretty smoothly within Jenkins. I haven't had time to figure out how to hook up code coverage, but what is there seems to work for now.